%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP625+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:25 PM UTC 2026
% Result : Theorem 100.20s 13.19s
% Output : CNFRefutation 100.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of formulae : 244 ( 32 unt; 0 def)
% Number of atoms : 1077 ( 139 equ)
% Maximal formula atoms : 90 ( 4 avg)
% Number of connectives : 1372 ( 539 ~; 574 |; 169 &)
% ( 9 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-4 aty)
% Number of functors : 26 ( 26 usr; 3 con; 0-6 aty)
% Number of variables : 490 ( 14 sgn 233 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_1(u1_group_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_group_1) ).
fof(free_g1_group_1,axiom,
! [X1,X2] :
( ( m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X2) )
=> ! [X3,X4] :
( g1_group_1(X1,X2) = g1_group_1(X3,X4)
=> ( X2 = X4
& X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
fof(abstractness_v1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( v1_group_1(X1)
=> X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
fof(dt_g1_group_1,axiom,
! [X1,X2] :
( ( m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X2) )
=> ( l1_group_1(g1_group_1(X1,X2))
& v1_group_1(g1_group_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_group_1) ).
fof(t16_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_autgroup) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(fc1_group_1,axiom,
! [X1,X2] :
( ( m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X2)
& ~ v1_xboole_0(X1) )
=> ( v1_group_1(g1_group_1(X1,X2))
& ~ v3_struct_0(g1_group_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_1) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(dt_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( m2_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(dt_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( m1_subset_1(X4,X1)
& m1_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
fof(redefinition_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( m1_subset_1(X4,X1)
& m1_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> k8_funct_2(X1,X2,X3,X4) = k1_funct_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(fc2_funct_1,axiom,
! [X1] :
( v1_funct_1(k6_relat_1(X1))
& v1_relat_1(k6_relat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(dt_k6_partfun1,axiom,
! [X1] :
( m2_relset_1(k6_partfun1(X1),X1,X1)
& v1_partfun1(k6_partfun1(X1),X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(dt_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k2_binop_1(X1,X2,X3,X4,X5,X6),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(dt_k1_fraenkel,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> m1_fraenkel(k1_fraenkel(X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_fraenkel) ).
fof(cc1_funct_2,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> ( ( v1_partfun1(X3,X1,X2)
& v1_funct_1(X3) )
=> ( v1_funct_2(X3,X1,X2)
& v1_funct_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(d5_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v2_group_1(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( X2 = k2_group_1(X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( k1_group_1(X1,X2,X3) = X3
& k1_group_1(X1,X3,X2) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_1) ).
fof(dt_k2_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(d1_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k1_group_1(X1,X2,X3) = k2_binop_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),u1_group_1(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_group_1) ).
fof(d2_group_3,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_group_3(X1,X2,X3) = k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_3) ).
fof(cc1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> ( ( v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v2_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_group_1) ).
fof(t16_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> k3_group_1(X1,k2_group_1(X1)) = k2_group_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_1) ).
fof(d4_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k4_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
=> ( r2_hidden(X3,X2)
<=> ? [X4] :
( ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> k8_funct_2(u1_struct_0(X1),u1_struct_0(X1),X3,X5) = k2_group_3(X1,X5,X4) )
& m1_subset_1(X4,u1_struct_0(X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_autgroup) ).
fof(dt_k4_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(t35_funct_1,axiom,
! [X1,X2] :
( r2_hidden(X2,X1)
=> k1_funct_1(k6_relat_1(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_partfun1,axiom,
? [X1] :
( v1_xboole_0(X1)
& v2_funct_1(X1)
& v1_funct_1(X1)
& v1_relat_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& X1 != X2
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(t11_funct_2,axiom,
! [X1,X2,X3] :
( ( m2_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3) )
=> ( ( X2 = k1_xboole_0
=> X1 = k1_xboole_0 )
=> r2_hidden(X3,k1_funct_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
fof(redefinition_k1_fraenkel,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
fof(c_0_37,plain,
! [X175,X176,X177] :
( ( m2_relset_1(X177,X175,X176)
| ~ m1_relset_1(X177,X175,X176) )
& ( m1_relset_1(X177,X175,X176)
| ~ m2_relset_1(X177,X175,X176) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_38,plain,
! [X103] :
( ( ~ l1_group_1(X103)
| m2_relset_1(u1_group_1(X103),k2_zfmisc_1(u1_struct_0(X103),u1_struct_0(X103)),u1_struct_0(X103)) )
& ( ~ l1_group_1(X103)
| v1_funct_2(u1_group_1(X103),k2_zfmisc_1(u1_struct_0(X103),u1_struct_0(X103)),u1_struct_0(X103)) )
& ( ~ l1_group_1(X103)
| v1_funct_1(u1_group_1(X103)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_group_1])])])]) ).
fof(c_0_39,plain,
! [X131,X132,X133,X134] :
( ( ~ m1_relset_1(X132,k2_zfmisc_1(X131,X131),X131)
| ~ v1_funct_2(X132,k2_zfmisc_1(X131,X131),X131)
| ~ v1_funct_1(X132)
| g1_group_1(X131,X132) != g1_group_1(X133,X134)
| X132 = X134 )
& ( ~ m1_relset_1(X132,k2_zfmisc_1(X131,X131),X131)
| ~ v1_funct_2(X132,k2_zfmisc_1(X131,X131),X131)
| ~ v1_funct_1(X132)
| g1_group_1(X131,X132) != g1_group_1(X133,X134)
| X131 = X133 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_group_1])])])])]) ).
cnf(c_0_40,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
( ~ l1_group_1(X1)
| m2_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,plain,
( ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X3)
| g1_group_1(X1,X3) != g1_group_1(X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
( ~ l1_group_1(X1)
| v1_funct_2(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( ~ l1_group_1(X1)
| v1_funct_1(u1_group_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( ~ l1_group_1(X1)
| m1_relset_1(u1_group_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_46,plain,
! [X8] :
( X8 = g1_group_1(u1_struct_0(X8),u1_group_1(X8))
| ~ v1_group_1(X8)
| ~ l1_group_1(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_group_1])])]) ).
fof(c_0_47,plain,
! [X66,X67] :
( ( ~ m1_relset_1(X67,k2_zfmisc_1(X66,X66),X66)
| ~ v1_funct_2(X67,k2_zfmisc_1(X66,X66),X66)
| ~ v1_funct_1(X67)
| l1_group_1(g1_group_1(X66,X67)) )
& ( ~ m1_relset_1(X67,k2_zfmisc_1(X66,X66),X66)
| ~ v1_funct_2(X67,k2_zfmisc_1(X66,X66),X66)
| ~ v1_funct_1(X67)
| v1_group_1(g1_group_1(X66,X67)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g1_group_1])])])]) ).
cnf(c_0_48,plain,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(X1),u1_group_1(X1)) != g1_group_1(X2,X3)
| u1_struct_0(X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_49,plain,
( ~ v1_group_1(X1)
| ~ l1_group_1(X1)
| X1 = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,plain,
( ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X2)
| v1_group_1(g1_group_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,plain,
( ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X2)
| l1_group_1(g1_group_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( ~ v1_group_1(g1_group_1(X1,X2))
| ~ l1_group_1(g1_group_1(X1,X2))
| u1_struct_0(g1_group_1(X1,X2)) = X1 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_53,plain,
( ~ l1_group_1(X1)
| v1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_54,plain,
( ~ l1_group_1(X1)
| l1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_44]),c_0_45]) ).
fof(c_0_55,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(assume_negation,[status(cth)],[t16_autgroup]) ).
cnf(c_0_56,plain,
( ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X1)
| g1_group_1(X3,X1) != g1_group_1(X4,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_57,plain,
( ~ l1_group_1(X1)
| u1_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) = u1_struct_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
fof(c_0_58,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
cnf(c_0_59,plain,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(X1),u1_group_1(X1)) != g1_group_1(X3,X2)
| u1_group_1(X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_60,plain,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(X1),u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))) = g1_group_1(u1_struct_0(X1),u1_group_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_57]),c_0_53]),c_0_54]) ).
fof(c_0_61,negated_conjecture,
( ~ m2_fraenkel(k6_partfun1(u1_struct_0(esk1_0)),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
cnf(c_0_62,plain,
( ~ l1_group_1(X2)
| ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(X1),u1_group_1(X1)) != g1_group_1(u1_struct_0(X2),u1_group_1(X2))
| u1_group_1(X1) = u1_group_1(g1_group_1(u1_struct_0(X2),u1_group_1(X2))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_64,plain,
( ~ l1_group_1(X1)
| v1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_57]),c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)) != g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))) = u1_group_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)) != g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| v1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
v1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_63])]) ).
cnf(c_0_68,plain,
( ~ v1_group_1(g1_group_1(X1,X2))
| ~ l1_group_1(g1_group_1(X1,X2))
| u1_group_1(g1_group_1(X1,X2)) = X2 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_49])]) ).
fof(c_0_69,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_70,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| u1_struct_0(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))) = u1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_71,plain,
( ~ v1_group_1(g1_group_1(X2,X1))
| ~ l1_group_1(g1_group_1(X2,X1))
| v1_funct_1(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_68]) ).
fof(c_0_72,plain,
! [X1,X2] :
( ( m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X2)
& ~ v1_xboole_0(X1) )
=> ( v1_group_1(g1_group_1(X1,X2))
& ~ v3_struct_0(g1_group_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_group_1]) ).
fof(c_0_73,plain,
! [X127] :
( ~ v1_xboole_0(u1_struct_0(X127))
| ~ l1_struct_0(X127)
| v3_struct_0(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
fof(c_0_74,plain,
! [X92] :
( l1_struct_0(X92)
| ~ l1_group_1(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])])]) ).
fof(c_0_75,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( m2_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_fraenkel]) ).
fof(c_0_76,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
fof(c_0_77,plain,
! [X1,X2,X3,X4] :
( ( m1_subset_1(X4,X1)
& m1_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
inference(fof_simplification,[status(thm)],[dt_k8_funct_2]) ).
fof(c_0_78,plain,
! [X1,X2,X3,X4] :
( ( m1_subset_1(X4,X1)
& m1_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3)
& ~ v1_xboole_0(X1) )
=> k8_funct_2(X1,X2,X3,X4) = k1_funct_1(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k8_funct_2]) ).
fof(c_0_79,plain,
! [X128] :
( v1_funct_1(k6_relat_1(X128))
& v1_relat_1(k6_relat_1(X128)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_80,plain,
! [X166] : k6_partfun1(X166) = k6_relat_1(X166),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(c_0_81,plain,
! [X86] :
( m2_relset_1(k6_partfun1(X86),X86,X86)
& v1_partfun1(k6_partfun1(X86),X86,X86) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
fof(c_0_82,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k2_binop_1(X1,X2,X3,X4,X5,X6),X3) ),
inference(fof_simplification,[status(thm)],[dt_k2_binop_1]) ).
fof(c_0_83,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1]) ).
cnf(c_0_84,negated_conjecture,
u1_struct_0(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))) = u1_struct_0(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_54]),c_0_63])]) ).
cnf(c_0_85,plain,
( ~ l1_group_1(X1)
| ~ l1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))))
| v1_funct_1(u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))) ),
inference(spm,[status(thm)],[c_0_71,c_0_64]) ).
cnf(c_0_86,plain,
( ~ l1_group_1(X1)
| l1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_57]),c_0_54]) ).
fof(c_0_87,plain,
! [X125,X126] :
( ( ~ m1_relset_1(X126,k2_zfmisc_1(X125,X125),X125)
| ~ v1_funct_2(X126,k2_zfmisc_1(X125,X125),X125)
| ~ v1_funct_1(X126)
| v1_xboole_0(X125)
| v1_group_1(g1_group_1(X125,X126)) )
& ( ~ m1_relset_1(X126,k2_zfmisc_1(X125,X125),X125)
| ~ v1_funct_2(X126,k2_zfmisc_1(X125,X125),X125)
| ~ v1_funct_1(X126)
| v1_xboole_0(X125)
| ~ v3_struct_0(g1_group_1(X125,X126)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])]) ).
cnf(c_0_88,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_89,plain,
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_90,plain,
! [X96,X97,X98,X99] :
( ( ~ m1_fraenkel(X98,X96,X97)
| v1_xboole_0(X97)
| ~ m2_fraenkel(X99,X96,X97,X98)
| m2_relset_1(X99,X96,X97) )
& ( ~ m1_fraenkel(X98,X96,X97)
| v1_xboole_0(X97)
| ~ m2_fraenkel(X99,X96,X97,X98)
| v1_funct_2(X99,X96,X97) )
& ( ~ m1_fraenkel(X98,X96,X97)
| v1_xboole_0(X97)
| ~ m2_fraenkel(X99,X96,X97,X98)
| v1_funct_1(X99) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])])]) ).
fof(c_0_91,plain,
! [X171,X172,X173,X174] :
( ( ~ m1_fraenkel(X173,X171,X172)
| v1_xboole_0(X172)
| m2_fraenkel(X174,X171,X172,X173)
| ~ m1_subset_1(X174,X173) )
& ( ~ m1_fraenkel(X173,X171,X172)
| v1_xboole_0(X172)
| m1_subset_1(X174,X173)
| ~ m2_fraenkel(X174,X171,X172,X173) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])])]) ).
fof(c_0_92,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> m1_fraenkel(k1_fraenkel(X1,X2),X1,X2) ),
inference(fof_simplification,[status(thm)],[dt_k1_fraenkel]) ).
fof(c_0_93,plain,
! [X88,X89,X90,X91] :
( m1_subset_1(k8_funct_2(X88,X89,X90,X91),X89)
| ~ m1_subset_1(X91,X88)
| ~ m1_relset_1(X90,X88,X89)
| ~ v1_funct_2(X90,X88,X89)
| ~ v1_funct_1(X90)
| v1_xboole_0(X88) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
fof(c_0_94,plain,
! [X167,X168,X169,X170] :
( k8_funct_2(X167,X168,X169,X170) = k1_funct_1(X169,X170)
| ~ m1_subset_1(X170,X167)
| ~ m1_relset_1(X169,X167,X168)
| ~ v1_funct_2(X169,X167,X168)
| ~ v1_funct_1(X169)
| v1_xboole_0(X167) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])]) ).
fof(c_0_95,plain,
! [X14,X15,X16] :
( ( ~ m1_relset_1(X16,X14,X15)
| ~ v1_partfun1(X16,X14,X15)
| ~ v1_funct_1(X16)
| v1_funct_2(X16,X14,X15) )
& ( ~ m1_relset_1(X16,X14,X15)
| ~ v1_partfun1(X16,X14,X15)
| ~ v1_funct_1(X16)
| v1_funct_1(X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])])]) ).
cnf(c_0_96,plain,
v1_funct_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_97,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_98,plain,
m2_relset_1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_99,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).
fof(c_0_100,plain,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v2_group_1(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( X2 = k2_group_1(X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( k1_group_1(X1,X2,X3) = X3
& k1_group_1(X1,X3,X2) = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d5_group_1]) ).
fof(c_0_101,plain,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_group_1]) ).
fof(c_0_102,plain,
! [X73,X74,X75,X76,X77,X78] :
( m1_subset_1(k2_binop_1(X73,X74,X75,X76,X77,X78),X75)
| ~ m1_subset_1(X78,X74)
| ~ m1_subset_1(X77,X73)
| ~ m1_relset_1(X76,k2_zfmisc_1(X73,X74),X75)
| ~ v1_funct_2(X76,k2_zfmisc_1(X73,X74),X75)
| ~ v1_funct_1(X76)
| v1_xboole_0(X74)
| v1_xboole_0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])]) ).
fof(c_0_103,plain,
! [X160,X161,X162,X163,X164,X165] :
( k2_binop_1(X160,X161,X162,X163,X164,X165) = k1_binop_1(X163,X164,X165)
| ~ m1_subset_1(X165,X161)
| ~ m1_subset_1(X164,X160)
| ~ m1_relset_1(X163,k2_zfmisc_1(X160,X161),X162)
| ~ v1_funct_2(X163,k2_zfmisc_1(X160,X161),X162)
| ~ v1_funct_1(X163)
| v1_xboole_0(X161)
| v1_xboole_0(X160) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])]) ).
cnf(c_0_104,plain,
( ~ v1_group_1(g1_group_1(X2,X1))
| ~ l1_group_1(g1_group_1(X2,X1))
| v1_funct_2(X1,k2_zfmisc_1(u1_struct_0(g1_group_1(X2,X1)),u1_struct_0(g1_group_1(X2,X1))),u1_struct_0(g1_group_1(X2,X1))) ),
inference(spm,[status(thm)],[c_0_43,c_0_68]) ).
cnf(c_0_105,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))))) ),
inference(spm,[status(thm)],[c_0_54,c_0_84]) ).
cnf(c_0_106,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_107,plain,
( ~ v1_group_1(g1_group_1(X2,X1))
| ~ l1_group_1(g1_group_1(X2,X1))
| m1_relset_1(X1,k2_zfmisc_1(u1_struct_0(g1_group_1(X2,X1)),u1_struct_0(g1_group_1(X2,X1))),u1_struct_0(g1_group_1(X2,X1))) ),
inference(spm,[status(thm)],[c_0_45,c_0_68]) ).
cnf(c_0_108,plain,
( ~ l1_group_1(X1)
| v1_funct_1(u1_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_109,plain,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k1_group_1(X1,X2,X3) = k2_binop_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),u1_group_1(X1),X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[d1_group_1]) ).
cnf(c_0_110,plain,
( ~ v1_group_1(g1_group_1(X3,X1))
| ~ l1_group_1(g1_group_1(X3,X1))
| g1_group_1(u1_struct_0(g1_group_1(X3,X1)),X1) != g1_group_1(X4,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_59,c_0_68]) ).
cnf(c_0_111,plain,
( ~ m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X2)
| ~ v3_struct_0(g1_group_1(X1,X2))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_112,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_113,plain,
( ~ l1_group_1(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_114,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_115,plain,
( ~ m1_fraenkel(X2,X3,X4)
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X4)
| m2_fraenkel(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
fof(c_0_116,plain,
! [X68,X69] :
( m1_fraenkel(k1_fraenkel(X68,X69),X68,X69)
| v1_xboole_0(X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])]) ).
cnf(c_0_117,plain,
( ~ m1_subset_1(X4,X1)
| ~ m1_relset_1(X2,X1,X3)
| ~ v1_funct_2(X2,X1,X3)
| ~ v1_funct_1(X2)
| m1_subset_1(k8_funct_2(X1,X3,X2,X4),X3)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_118,plain,
( ~ m1_subset_1(X4,X1)
| ~ m1_relset_1(X2,X1,X3)
| ~ v1_funct_2(X2,X1,X3)
| ~ v1_funct_1(X2)
| k8_funct_2(X1,X3,X2,X4) = k1_funct_1(X2,X4)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_119,plain,
( ~ m1_relset_1(X1,X2,X3)
| ~ v1_partfun1(X1,X2,X3)
| ~ v1_funct_1(X1)
| v1_funct_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_120,plain,
v1_partfun1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_121,plain,
v1_funct_1(k6_partfun1(X1)),
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_122,plain,
m1_relset_1(k6_partfun1(X1),X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_98]) ).
fof(c_0_123,plain,
! [X93,X94,X95] :
( ( ~ m1_fraenkel(X95,X93,X94)
| v1_fraenkel(X95) )
& ( ~ m1_fraenkel(X95,X93,X94)
| ~ v1_xboole_0(X95) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])])]) ).
fof(c_0_124,plain,
! [X60,X61,X62] :
( ( ~ l1_group_1(X60)
| v3_struct_0(X60)
| ~ v2_group_1(X60)
| ~ m1_subset_1(X61,u1_struct_0(X60))
| X61 = k2_group_1(X60)
| k1_group_1(X60,X61,esk7_2(X60,X61)) != esk7_2(X60,X61)
| k1_group_1(X60,esk7_2(X60,X61),X61) != esk7_2(X60,X61) )
& ( ~ l1_group_1(X60)
| v3_struct_0(X60)
| ~ v2_group_1(X60)
| ~ m1_subset_1(X61,u1_struct_0(X60))
| X61 = k2_group_1(X60)
| m1_subset_1(esk7_2(X60,X61),u1_struct_0(X60)) )
& ( ~ l1_group_1(X60)
| v3_struct_0(X60)
| ~ v2_group_1(X60)
| ~ m1_subset_1(X61,u1_struct_0(X60))
| X61 != k2_group_1(X60)
| ~ m1_subset_1(X62,u1_struct_0(X60))
| k1_group_1(X60,X61,X62) = X62 )
& ( ~ l1_group_1(X60)
| v3_struct_0(X60)
| ~ v2_group_1(X60)
| ~ m1_subset_1(X61,u1_struct_0(X60))
| X61 != k2_group_1(X60)
| ~ m1_subset_1(X62,u1_struct_0(X60))
| k1_group_1(X60,X62,X61) = X62 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])])])]) ).
fof(c_0_125,plain,
! [X79] :
( m1_subset_1(k2_group_1(X79),u1_struct_0(X79))
| ~ l1_group_1(X79)
| v3_struct_0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])]) ).
fof(c_0_126,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_group_3(X1,X2,X3) = k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X2),X3) ) ) ),
inference(fof_simplification,[status(thm)],[d2_group_3]) ).
fof(c_0_127,plain,
! [X1] :
( l1_group_1(X1)
=> ( ( v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v2_group_1(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_group_1]) ).
cnf(c_0_128,plain,
( ~ m1_subset_1(X6,X2)
| ~ m1_subset_1(X5,X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_1(X3)
| m1_subset_1(k2_binop_1(X1,X2,X4,X3,X5,X6),X4)
| v1_xboole_0(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_129,plain,
( ~ m1_subset_1(X6,X2)
| ~ m1_subset_1(X5,X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_1(X3)
| k2_binop_1(X1,X2,X4,X3,X5,X6) = k1_binop_1(X3,X5,X6)
| v1_xboole_0(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_130,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| v1_funct_2(u1_group_1(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_84]),c_0_67])]) ).
cnf(c_0_131,negated_conjecture,
l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_49]),c_0_63]),c_0_106])]) ).
cnf(c_0_132,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| m1_relset_1(u1_group_1(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_84]),c_0_67])]) ).
cnf(c_0_133,negated_conjecture,
( ~ l1_group_1(X1)
| g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)) != g1_group_1(u1_struct_0(X1),u1_group_1(X1))
| v1_funct_1(u1_group_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_108,c_0_65]) ).
fof(c_0_134,plain,
! [X42,X43,X44] :
( k1_group_1(X42,X43,X44) = k2_binop_1(u1_struct_0(X42),u1_struct_0(X42),u1_struct_0(X42),u1_group_1(X42),X43,X44)
| ~ m1_subset_1(X44,u1_struct_0(X42))
| ~ m1_subset_1(X43,u1_struct_0(X42))
| ~ l1_group_1(X42)
| v3_struct_0(X42) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])]) ).
cnf(c_0_135,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)) != g1_group_1(X2,X1)
| u1_group_1(esk1_0) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_84]),c_0_67])]) ).
cnf(c_0_136,plain,
( ~ v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ l1_group_1(X1)
| v1_xboole_0(u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_137,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_63])]) ).
cnf(c_0_138,plain,
( ~ m1_subset_1(X1,X4)
| ~ m1_fraenkel(X4,X2,X3)
| v1_xboole_0(X3)
| m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_139,plain,
( m1_fraenkel(k1_fraenkel(X2,X1),X2,X1)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_140,plain,
( ~ m1_subset_1(X3,X1)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,X1,X4)
| ~ v1_funct_2(X2,X1,X4)
| m1_subset_1(k1_funct_1(X2,X3),X4)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_141,plain,
v1_funct_2(k6_partfun1(X1),X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]),c_0_122])]) ).
cnf(c_0_142,plain,
( ~ m1_fraenkel(X1,X2,X3)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_143,plain,
( ~ l1_group_1(X1)
| ~ v2_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| X3 != k2_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,X2,X3) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_144,plain,
( ~ l1_group_1(X1)
| m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
fof(c_0_145,plain,
! [X45,X46,X47] :
( k2_group_3(X45,X46,X47) = k1_group_1(X45,k1_group_1(X45,k3_group_1(X45,X47),X46),X47)
| ~ m1_subset_1(X47,u1_struct_0(X45))
| ~ m1_subset_1(X46,u1_struct_0(X45))
| ~ l1_group_1(X45)
| ~ v4_group_1(X45)
| ~ v3_group_1(X45)
| v3_struct_0(X45) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])]) ).
fof(c_0_146,plain,
! [X17] :
( ( ~ l1_group_1(X17)
| ~ v3_group_1(X17)
| v3_struct_0(X17)
| v2_group_1(X17) )
& ( ~ l1_group_1(X17)
| ~ v3_group_1(X17)
| v3_struct_0(X17)
| ~ v3_struct_0(X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])]) ).
cnf(c_0_147,plain,
( ~ m1_subset_1(X4,X1)
| ~ m1_subset_1(X5,X2)
| ~ v1_funct_1(X3)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X6)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X6)
| m1_subset_1(k1_binop_1(X3,X4,X5),X6)
| v1_xboole_0(X2)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_148,negated_conjecture,
v1_funct_2(u1_group_1(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]) ).
cnf(c_0_149,negated_conjecture,
m1_relset_1(u1_group_1(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_49]),c_0_63]),c_0_106])]) ).
cnf(c_0_150,negated_conjecture,
v1_funct_1(u1_group_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_133]),c_0_63])]) ).
cnf(c_0_151,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| k1_group_1(X1,X2,X3) = k2_binop_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),u1_group_1(X1),X2,X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_152,negated_conjecture,
( g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)) != g1_group_1(X2,X1)
| u1_group_1(esk1_0) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_54]),c_0_63])]) ).
cnf(c_0_153,negated_conjecture,
( ~ v3_struct_0(g1_group_1(u1_struct_0(esk1_0),u1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))))
| ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_84]),c_0_137]) ).
fof(c_0_154,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> k3_group_1(X1,k2_group_1(X1)) = k2_group_1(X1) ),
inference(fof_simplification,[status(thm)],[t16_group_1]) ).
fof(c_0_155,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
=> ( X2 = k4_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
=> ( r2_hidden(X3,X2)
<=> ? [X4] :
( ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> k8_funct_2(u1_struct_0(X1),u1_struct_0(X1),X3,X5) = k2_group_3(X1,X5,X4) )
& m1_subset_1(X4,u1_struct_0(X1)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_autgroup]) ).
fof(c_0_156,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_autgroup]) ).
cnf(c_0_157,plain,
( ~ m1_subset_1(X1,k1_fraenkel(X2,X3))
| v1_xboole_0(X3)
| m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_158,plain,
( ~ m1_subset_1(X2,X1)
| m1_subset_1(k1_funct_1(k6_partfun1(X1),X2),X1)
| v1_xboole_0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_122]),c_0_121])]) ).
cnf(c_0_159,plain,
( ~ v1_xboole_0(k1_fraenkel(X2,X1))
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_139]) ).
fof(c_0_160,plain,
! [X187,X188] :
( k1_funct_1(k6_relat_1(X187),X188) = X188
| ~ r2_hidden(X188,X187) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])])]) ).
cnf(c_0_161,plain,
( ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v2_group_1(X1)
| v3_struct_0(X1)
| k1_group_1(X1,X2,k2_group_1(X1)) = X2 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_143]),c_0_144]) ).
cnf(c_0_162,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| k2_group_3(X1,X2,X3) = k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X2),X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_163,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| v2_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_164,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| m1_subset_1(k1_binop_1(u1_group_1(esk1_0),X1,X2),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_150])]),c_0_137]) ).
cnf(c_0_165,plain,
( ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_binop_1(u1_group_1(X1),X2,X3) = k1_group_1(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_151]),c_0_44]),c_0_45]),c_0_43]),c_0_113]) ).
cnf(c_0_166,plain,
( ~ l1_group_1(X1)
| v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| m1_subset_1(k2_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1))),u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_57]),c_0_54]) ).
cnf(c_0_167,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| u1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))) = u1_group_1(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_49])]),c_0_67])]) ).
cnf(c_0_168,negated_conjecture,
~ v3_struct_0(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_49]),c_0_63]),c_0_106])]) ).
fof(c_0_169,plain,
! [X182] :
( k3_group_1(X182,k2_group_1(X182)) = k2_group_1(X182)
| ~ l1_group_1(X182)
| ~ v4_group_1(X182)
| ~ v3_group_1(X182)
| v3_struct_0(X182) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])])]) ).
fof(c_0_170,plain,
! [X48,X49,X50,X52,X53,X56,X59] :
( ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 = k4_autgroup(X48)
| r2_hidden(esk4_2(X48,X49),X49)
| k8_funct_2(u1_struct_0(X48),u1_struct_0(X48),esk4_2(X48,X49),X59) = k2_group_3(X48,X59,esk6_2(X48,X49))
| ~ m1_subset_1(X59,u1_struct_0(X48)) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 = k4_autgroup(X48)
| r2_hidden(esk4_2(X48,X49),X49)
| m1_subset_1(esk6_2(X48,X49),u1_struct_0(X48)) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 = k4_autgroup(X48)
| ~ r2_hidden(esk4_2(X48,X49),X49)
| ~ m1_subset_1(X56,u1_struct_0(X48))
| k8_funct_2(u1_struct_0(X48),u1_struct_0(X48),esk4_2(X48,X49),esk5_3(X48,X49,X56)) != k2_group_3(X48,esk5_3(X48,X49,X56),X56) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 = k4_autgroup(X48)
| ~ r2_hidden(esk4_2(X48,X49),X49)
| ~ m1_subset_1(X56,u1_struct_0(X48))
| m1_subset_1(esk5_3(X48,X49,X56),u1_struct_0(X48)) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 = k4_autgroup(X48)
| m2_fraenkel(esk4_2(X48,X49),u1_struct_0(X48),u1_struct_0(X48),k1_fraenkel(u1_struct_0(X48),u1_struct_0(X48))) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 != k4_autgroup(X48)
| ~ m2_fraenkel(X50,u1_struct_0(X48),u1_struct_0(X48),k1_fraenkel(u1_struct_0(X48),u1_struct_0(X48)))
| r2_hidden(X50,X49)
| ~ m1_subset_1(X53,u1_struct_0(X48))
| k8_funct_2(u1_struct_0(X48),u1_struct_0(X48),X50,esk3_4(X48,X49,X50,X53)) != k2_group_3(X48,esk3_4(X48,X49,X50,X53),X53) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 != k4_autgroup(X48)
| ~ m2_fraenkel(X50,u1_struct_0(X48),u1_struct_0(X48),k1_fraenkel(u1_struct_0(X48),u1_struct_0(X48)))
| r2_hidden(X50,X49)
| ~ m1_subset_1(X53,u1_struct_0(X48))
| m1_subset_1(esk3_4(X48,X49,X50,X53),u1_struct_0(X48)) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 != k4_autgroup(X48)
| ~ m2_fraenkel(X50,u1_struct_0(X48),u1_struct_0(X48),k1_fraenkel(u1_struct_0(X48),u1_struct_0(X48)))
| ~ r2_hidden(X50,X49)
| k8_funct_2(u1_struct_0(X48),u1_struct_0(X48),X50,X52) = k2_group_3(X48,X52,esk2_3(X48,X49,X50))
| ~ m1_subset_1(X52,u1_struct_0(X48)) )
& ( ~ l1_group_1(X48)
| ~ v4_group_1(X48)
| ~ v3_group_1(X48)
| ~ v1_group_1(X48)
| v3_struct_0(X48)
| ~ m1_fraenkel(X49,u1_struct_0(X48),u1_struct_0(X48))
| X49 != k4_autgroup(X48)
| ~ m2_fraenkel(X50,u1_struct_0(X48),u1_struct_0(X48),k1_fraenkel(u1_struct_0(X48),u1_struct_0(X48)))
| ~ r2_hidden(X50,X49)
| m1_subset_1(esk2_3(X48,X49,X50),u1_struct_0(X48)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])])])])])]) ).
fof(c_0_171,plain,
! [X85] :
( m1_fraenkel(k4_autgroup(X85),u1_struct_0(X85),u1_struct_0(X85))
| ~ l1_group_1(X85)
| ~ v4_group_1(X85)
| ~ v3_group_1(X85)
| ~ v1_group_1(X85)
| v3_struct_0(X85) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])]) ).
cnf(c_0_172,plain,
( ~ m1_subset_1(X3,k1_fraenkel(X1,X2))
| v1_xboole_0(X2)
| m2_relset_1(k1_funct_1(k6_partfun1(k1_fraenkel(X1,X2)),X3),X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159]) ).
cnf(c_0_173,plain,
( ~ r2_hidden(X1,X2)
| k1_funct_1(k6_relat_1(X2),X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
fof(c_0_174,plain,
! [X183,X184] :
( m1_subset_1(X183,X184)
| ~ r2_hidden(X183,X184) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_175,plain,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(k1_group_1(X1,k3_group_1(X1,k2_group_1(X1)),X2),u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,k3_group_1(X1,k2_group_1(X1)),X2) = k2_group_3(X1,X2,k2_group_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_144]),c_0_163]) ).
cnf(c_0_176,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| m1_subset_1(k1_group_1(esk1_0,X1,X2),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_63])]),c_0_112]) ).
cnf(c_0_177,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_178,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_179,negated_conjecture,
( ~ l1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| m1_subset_1(k2_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_84]),c_0_84]),c_0_84]),c_0_168]) ).
cnf(c_0_180,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| k3_group_1(X1,k2_group_1(X1)) = k2_group_1(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_181,plain,
( ~ l1_group_1(X1)
| ~ v2_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| X2 != k2_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_182,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1))
| X3 != k4_autgroup(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| k8_funct_2(u1_struct_0(X1),u1_struct_0(X1),X2,esk3_4(X1,X3,X2,X4)) != k2_group_3(X1,esk3_4(X1,X3,X2,X4),X4)
| v3_struct_0(X1)
| r2_hidden(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_183,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_184,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m1_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1))
| X2 != k4_autgroup(X1)
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| v3_struct_0(X1)
| r2_hidden(X3,X2)
| m1_subset_1(esk3_4(X1,X2,X3,X4),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_185,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_186,plain,
( ~ m1_subset_1(X3,k1_fraenkel(X1,X2))
| v1_xboole_0(X2)
| m1_relset_1(k1_funct_1(k6_partfun1(k1_fraenkel(X1,X2)),X3),X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_172]) ).
cnf(c_0_187,plain,
( ~ r2_hidden(X1,X2)
| k1_funct_1(k6_partfun1(X2),X1) = X1 ),
inference(rw,[status(thm)],[c_0_173,c_0_97]) ).
cnf(c_0_188,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
fof(c_0_189,plain,
! [X185,X186] :
( r2_hidden(X185,X186)
| v1_xboole_0(X186)
| ~ m1_subset_1(X185,X186) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_190,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| v1_funct_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_191,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(k3_group_1(esk1_0,k2_group_1(esk1_0)),u1_struct_0(esk1_0))
| k1_group_1(esk1_0,k3_group_1(esk1_0,k2_group_1(esk1_0)),X1) = k2_group_3(esk1_0,X1,k2_group_1(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_63]),c_0_177]),c_0_178])]),c_0_112]) ).
cnf(c_0_192,negated_conjecture,
m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_49]),c_0_63]),c_0_106])]) ).
cnf(c_0_193,plain,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(k1_group_1(X1,k2_group_1(X1),X2),u1_struct_0(X1))
| v3_struct_0(X1)
| k2_group_3(X1,X2,k2_group_1(X1)) = k1_group_1(X1,k2_group_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_175,c_0_180]) ).
cnf(c_0_194,plain,
( ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v2_group_1(X1)
| v3_struct_0(X1)
| k1_group_1(X1,k2_group_1(X1),X2) = X2 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_181]),c_0_144]) ).
cnf(c_0_195,plain,
( ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| k8_funct_2(u1_struct_0(X2),u1_struct_0(X2),X1,esk3_4(X2,k4_autgroup(X2),X1,X3)) != k2_group_3(X2,esk3_4(X2,k4_autgroup(X2),X1,X3),X3)
| v3_struct_0(X2)
| r2_hidden(X1,k4_autgroup(X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_182]),c_0_183]) ).
cnf(c_0_196,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| v3_struct_0(X1)
| r2_hidden(X2,k4_autgroup(X1))
| m1_subset_1(esk3_4(X1,k4_autgroup(X1),X2,X3),u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_184]),c_0_183]) ).
cnf(c_0_197,plain,
( ~ v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ l1_group_1(X1)
| v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_136,c_0_49]) ).
cnf(c_0_198,plain,
( ~ m1_subset_1(X2,X3)
| ~ m1_fraenkel(X3,X4,X1)
| v1_funct_1(X2)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_185,c_0_115]) ).
cnf(c_0_199,plain,
( ~ r2_hidden(X1,k1_fraenkel(X2,X3))
| v1_xboole_0(X3)
| m1_relset_1(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]) ).
cnf(c_0_200,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_201,plain,
( ~ m1_subset_1(X1,X4)
| ~ m1_fraenkel(X4,X2,X3)
| v1_xboole_0(X3)
| v1_funct_2(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_190,c_0_115]) ).
cnf(c_0_202,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| k2_group_3(esk1_0,X1,k2_group_1(esk1_0)) = k1_group_1(esk1_0,k2_group_1(esk1_0),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_180]),c_0_192]),c_0_63]),c_0_177]),c_0_178])]),c_0_112]) ).
cnf(c_0_203,plain,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k2_group_3(X1,X2,k2_group_1(X1)) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_163]) ).
cnf(c_0_204,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,u1_struct_0(X1),u1_struct_0(X1))
| ~ v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))
| k1_funct_1(X2,esk3_4(X1,k4_autgroup(X1),X2,X3)) != k2_group_3(X1,esk3_4(X1,k4_autgroup(X1),X2,X3),X3)
| r2_hidden(X2,k4_autgroup(X1))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_118]),c_0_196]),c_0_197]) ).
cnf(c_0_205,plain,
( ~ m1_subset_1(X2,k1_fraenkel(X3,X1))
| v1_funct_1(X2)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_198,c_0_139]) ).
cnf(c_0_206,plain,
( ~ m1_subset_1(X1,k1_fraenkel(X2,X3))
| v1_xboole_0(X3)
| m1_relset_1(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_159]) ).
cnf(c_0_207,plain,
( ~ m1_subset_1(X1,k1_fraenkel(X2,X3))
| v1_xboole_0(X3)
| v1_funct_2(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_201,c_0_139]) ).
cnf(c_0_208,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| k1_group_1(esk1_0,k2_group_1(esk1_0),X1) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_63]),c_0_177]),c_0_178])]),c_0_112]) ).
cnf(c_0_209,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| k1_funct_1(X2,esk3_4(X1,k4_autgroup(X1),X2,X3)) != k2_group_3(X1,esk3_4(X1,k4_autgroup(X1),X2,X3),X3)
| r2_hidden(X2,k4_autgroup(X1))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_115]),c_0_205]),c_0_206]),c_0_207]),c_0_139]) ).
cnf(c_0_210,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| k2_group_3(esk1_0,X1,k2_group_1(esk1_0)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_208]),c_0_63]),c_0_177]),c_0_178])]),c_0_112]) ).
cnf(c_0_211,negated_conjecture,
( ~ m1_subset_1(X1,k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))
| ~ m1_subset_1(esk3_4(esk1_0,k4_autgroup(esk1_0),X1,k2_group_1(esk1_0)),u1_struct_0(esk1_0))
| k1_funct_1(X1,esk3_4(esk1_0,k4_autgroup(esk1_0),X1,k2_group_1(esk1_0))) != esk3_4(esk1_0,k4_autgroup(esk1_0),X1,k2_group_1(esk1_0))
| r2_hidden(X1,k4_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_192]),c_0_63]),c_0_177]),c_0_178]),c_0_106])]),c_0_137]) ).
fof(c_0_212,plain,
! [X197] :
( X197 = k1_xboole_0
| ~ v1_xboole_0(X197) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_213,plain,
( v1_xboole_0(esk19_0)
& v2_funct_1(esk19_0)
& v1_funct_1(esk19_0)
& v1_relat_1(esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
fof(c_0_214,plain,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& X1 != X2
& v1_xboole_0(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
cnf(c_0_215,negated_conjecture,
( ~ r2_hidden(esk3_4(esk1_0,k4_autgroup(esk1_0),k6_partfun1(X1),k2_group_1(esk1_0)),X1)
| ~ m1_subset_1(k6_partfun1(X1),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))
| ~ m1_subset_1(esk3_4(esk1_0,k4_autgroup(esk1_0),k6_partfun1(X1),k2_group_1(esk1_0)),u1_struct_0(esk1_0))
| r2_hidden(k6_partfun1(X1),k4_autgroup(esk1_0)) ),
inference(spm,[status(thm)],[c_0_211,c_0_187]) ).
cnf(c_0_216,plain,
( ~ v3_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ v4_group_1(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| ~ l1_group_1(X1)
| v3_struct_0(g1_group_1(u1_struct_0(X1),u1_group_1(X1)))
| m1_fraenkel(k4_autgroup(g1_group_1(u1_struct_0(X1),u1_group_1(X1))),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_57]),c_0_53]),c_0_54]) ).
cnf(c_0_217,negated_conjecture,
u1_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))) = u1_group_1(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_131])]) ).
fof(c_0_218,plain,
! [X179,X180,X181] :
( ( ~ m2_relset_1(X181,X179,X180)
| ~ v1_funct_2(X181,X179,X180)
| ~ v1_funct_1(X181)
| r2_hidden(X181,k1_funct_2(X179,X180))
| X179 != k1_xboole_0 )
& ( ~ m2_relset_1(X181,X179,X180)
| ~ v1_funct_2(X181,X179,X180)
| ~ v1_funct_1(X181)
| r2_hidden(X181,k1_funct_2(X179,X180))
| X180 = k1_xboole_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t11_funct_2])])])]) ).
cnf(c_0_219,plain,
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_220,plain,
v1_xboole_0(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
fof(c_0_221,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_fraenkel]) ).
fof(c_0_222,plain,
! [X200,X201] :
( ~ v1_xboole_0(X201)
| X200 = X201
| ~ v1_xboole_0(X200) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])])]) ).
cnf(c_0_223,negated_conjecture,
( ~ m1_subset_1(k6_partfun1(X1),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))
| ~ m1_subset_1(esk3_4(esk1_0,k4_autgroup(esk1_0),k6_partfun1(X1),k2_group_1(esk1_0)),X1)
| ~ m1_subset_1(esk3_4(esk1_0,k4_autgroup(esk1_0),k6_partfun1(X1),k2_group_1(esk1_0)),u1_struct_0(esk1_0))
| r2_hidden(k6_partfun1(X1),k4_autgroup(esk1_0))
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_215,c_0_200]) ).
cnf(c_0_224,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| r2_hidden(X2,k4_autgroup(X1))
| m1_subset_1(esk3_4(X1,k4_autgroup(X1),X2,X3),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_115]),c_0_139]),c_0_197]) ).
cnf(c_0_225,negated_conjecture,
~ m2_fraenkel(k6_partfun1(u1_struct_0(esk1_0)),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_226,negated_conjecture,
( ~ v3_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| ~ v4_group_1(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0)))
| m1_fraenkel(k4_autgroup(g1_group_1(u1_struct_0(esk1_0),u1_group_1(esk1_0))),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_84]),c_0_84]),c_0_84]),c_0_84]),c_0_131]),c_0_84]),c_0_84])]),c_0_168]) ).
cnf(c_0_227,plain,
( ~ m2_relset_1(X2,X3,X1)
| ~ v1_funct_2(X2,X3,X1)
| ~ v1_funct_1(X2)
| r2_hidden(X2,k1_funct_2(X3,X1))
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_228,plain,
k1_xboole_0 = esk19_0,
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
fof(c_0_229,plain,
! [X158,X159] :
( k1_fraenkel(X158,X159) = k1_funct_2(X158,X159)
| v1_xboole_0(X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_221])]) ).
cnf(c_0_230,plain,
( ~ v1_xboole_0(X2)
| ~ v1_xboole_0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_231,negated_conjecture,
( ~ m1_subset_1(k6_partfun1(X1),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))
| ~ m1_subset_1(esk3_4(esk1_0,k4_autgroup(esk1_0),k6_partfun1(X1),k2_group_1(esk1_0)),X1)
| r2_hidden(k6_partfun1(X1),k4_autgroup(esk1_0))
| v1_xboole_0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_192]),c_0_63]),c_0_177]),c_0_178]),c_0_106])]),c_0_137]) ).
cnf(c_0_232,negated_conjecture,
( ~ m1_subset_1(k6_partfun1(u1_struct_0(esk1_0)),k4_autgroup(esk1_0))
| ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_225,c_0_115]) ).
cnf(c_0_233,negated_conjecture,
m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_49]),c_0_177]),c_0_178]),c_0_63]),c_0_106])]) ).
cnf(c_0_234,plain,
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X3,X1)
| ~ m2_relset_1(X2,X3,X1)
| r2_hidden(X2,k1_funct_2(X3,X1))
| X1 = esk19_0 ),
inference(rw,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_235,plain,
( k1_fraenkel(X2,X1) = k1_funct_2(X2,X1)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_236,plain,
( ~ v1_xboole_0(X1)
| X1 = esk19_0 ),
inference(spm,[status(thm)],[c_0_230,c_0_220]) ).
cnf(c_0_237,negated_conjecture,
( ~ m1_subset_1(k6_partfun1(u1_struct_0(esk1_0)),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))
| r2_hidden(k6_partfun1(u1_struct_0(esk1_0)),k4_autgroup(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_224]),c_0_192]),c_0_63]),c_0_177]),c_0_178]),c_0_106])]),c_0_137]) ).
cnf(c_0_238,negated_conjecture,
~ m1_subset_1(k6_partfun1(u1_struct_0(esk1_0)),k4_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_233])]),c_0_137]) ).
cnf(c_0_239,plain,
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X3,X1)
| ~ m2_relset_1(X2,X3,X1)
| r2_hidden(X2,k1_fraenkel(X3,X1))
| X1 = esk19_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_236]) ).
cnf(c_0_240,negated_conjecture,
~ m1_subset_1(k6_partfun1(u1_struct_0(esk1_0)),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_237]),c_0_238]) ).
cnf(c_0_241,plain,
( ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X3,X1)
| ~ m2_relset_1(X2,X3,X1)
| m1_subset_1(X2,k1_fraenkel(X3,X1))
| X1 = esk19_0 ),
inference(spm,[status(thm)],[c_0_188,c_0_239]) ).
cnf(c_0_242,negated_conjecture,
u1_struct_0(esk1_0) = esk19_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_98]),c_0_141]),c_0_121])]) ).
cnf(c_0_243,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_242]),c_0_220])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP625+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:20:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.20/13.18 % Version: 3.5.1
% 100.20/13.18 % Preprocessing class: FSLSSMSSSSSNFFN.
% 100.20/13.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.20/13.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 100.20/13.18 % Starting new_bool_3 with 300s (1) cores
% 100.20/13.18 % Starting new_bool_1 with 300s (1) cores
% 100.20/13.18 % Starting sh5l with 300s (1) cores
% 100.20/13.18 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1687164 completed with status 0
% 100.20/13.18 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 100.20/13.18 % Preprocessing class: FSLSSMSSSSSNFFN.
% 100.20/13.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.20/13.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 100.20/13.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 100.20/13.18 % No SInE strategy applied
% 100.20/13.18 % Search class: FGHSM-FSLM32-MFFFFFNN
% 100.20/13.18 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 100.20/13.18 % Starting SubtermCWHack with 136s (1) cores
% 100.20/13.18 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 100.20/13.18 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 100.20/13.19 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 100.20/13.19 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 100.20/13.19 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 1687175 completed with status 0
% 100.20/13.19 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 100.20/13.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 100.20/13.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.20/13.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 100.20/13.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 100.20/13.19 % No SInE strategy applied
% 100.20/13.19 % Search class: FGHSM-FSLM32-MFFFFFNN
% 100.20/13.19 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 100.20/13.19 % Starting SubtermCWHack with 136s (1) cores
% 100.20/13.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 100.20/13.19 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 100.20/13.19 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 100.20/13.19 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 100.20/13.19 % Preprocessing time : 0.004 s
% 100.20/13.19 % Presaturation interreduction done
% 100.20/13.19
% 100.20/13.19 % Proof found!
% 100.20/13.19 % SZS status Theorem
% 100.20/13.19 % SZS output start CNFRefutation
% See solution above
% 100.20/13.19 % Parsed axioms : 101
% 100.20/13.19 % Removed by relevancy pruning/SinE : 0
% 100.20/13.19 % Initial clauses : 192
% 100.20/13.19 % Removed in clause preprocessing : 30
% 100.20/13.19 % Initial clauses in saturation : 162
% 100.20/13.19 % Processed clauses : 20984
% 100.20/13.19 % ...of these trivial : 82
% 100.20/13.19 % ...subsumed : 15732
% 100.20/13.19 % ...remaining for further processing : 5170
% 100.20/13.19 % Other redundant clauses eliminated : 69
% 100.20/13.19 % Clauses deleted for lack of memory : 0
% 100.20/13.19 % Backward-subsumed : 697
% 100.20/13.19 % Backward-rewritten : 765
% 100.20/13.19 % Generated clauses : 149603
% 100.20/13.19 % ...of the previous two non-redundant : 139401
% 100.20/13.19 % ...aggressively subsumed : 0
% 100.20/13.19 % Contextual simplify-reflections : 944
% 100.20/13.19 % Paramodulations : 149484
% 100.20/13.19 % Factorizations : 0
% 100.20/13.19 % NegExts : 0
% 100.20/13.19 % Equation resolutions : 119
% 100.20/13.19 % Disequality decompositions : 0
% 100.20/13.19 % Total rewrite steps : 86311
% 100.20/13.19 % ...of those cached : 85624
% 100.20/13.19 % Propositional unsat checks : 1
% 100.20/13.19 % Propositional check models : 0
% 100.20/13.19 % Propositional check unsatisfiable : 0
% 100.20/13.19 % Propositional clauses : 0
% 100.20/13.19 % Propositional clauses after purity: 0
% 100.20/13.19 % Propositional unsat core size : 0
% 100.20/13.19 % Propositional preprocessing time : 0.000
% 100.20/13.19 % Propositional encoding time : 0.676
% 100.20/13.19 % Propositional solver time : 0.285
% 100.20/13.19 % Success case prop preproc time : 0.000
% 100.20/13.19 % Success case prop encoding time : 0.000
% 100.20/13.19 % Success case prop solver time : 0.000
% 100.20/13.19 % Current number of processed clauses : 3544
% 100.20/13.19 % Positive orientable unit clauses : 98
% 100.20/13.19 % Positive unorientable unit clauses: 1
% 100.20/13.19 % Negative unit clauses : 18
% 100.20/13.19 % Non-unit-clauses : 3427
% 100.20/13.19 % Current number of unprocessed clauses: 115646
% 100.20/13.19 % ...number of literals in the above : 750221
% 100.20/13.19 % Current number of archived formulas : 0
% 100.20/13.19 % Current number of archived clauses : 1621
% 100.20/13.19 % Clause-clause subsumption calls (NU) : 7199808
% 100.20/13.19 % Rec. Clause-clause subsumption calls : 1477640
% 100.20/13.19 % Non-unit clause-clause subsumptions : 15510
% 100.20/13.19 % Unit Clause-clause subsumption calls : 14465
% 100.20/13.19 % Rewrite failures with RHS unbound : 0
% 100.20/13.19 % BW rewrite match attempts : 97
% 100.20/13.19 % BW rewrite match successes : 23
% 100.20/13.19 % Condensation attempts : 0
% 100.20/13.19 % Condensation successes : 0
% 100.20/13.19 % Termbank termtop insertions : 7604809
% 100.20/13.19 % Search garbage collected termcells : 2230
% 100.20/13.19
% 100.20/13.19 % -------------------------------------------------
% 100.20/13.19 % User time : 12.264 s
% 100.20/13.19 % System time : 0.241 s
% 100.20/13.19 % Total time : 12.505 s
% 100.20/13.19 % Maximum resident set size: 4252 pages
% 100.20/13.19
% 100.20/13.19 % -------------------------------------------------
% 100.20/13.19 % User time : 60.723 s
% 100.20/13.19 % System time : 1.230 s
% 100.20/13.19 % Total time : 61.953 s
% 100.20/13.19 % Maximum resident set size: 4608 pages
% 100.20/13.19 % E exiting
%------------------------------------------------------------------------------